de Broglie combined Einstien’s E = mc 2 and Planck’s E = hv de Broglie combined Einstien’s E = mc 2 and Planck’s E = hv hv = mc 2 hv = mc 2 Substitute v = c/λ hc = mc 2 Substitute v = c/λ hc = mc 2 λ Divide both sides by c: h =mc Divide both sides by c: h =mc λ Or λ = h mc mc Wavelength could be predicted by the mass and speed of the particle. momentum

Challenge Problem 3 The diameter of a US penny is 19mm. The diameter of a silver atom is only 2.88 Å. How many silver atoms could be arranged side by side in a straight line across the diameter of a penny? (10 8 Å = 1cm) The diameter of a US penny is 19mm. The diameter of a silver atom is only 2.88 Å. How many silver atoms could be arranged side by side in a straight line across the diameter of a penny? (10 8 Å = 1cm)

Young woman or old woman? What do you see?

Review Light of a particular wavelength (λ) has a particular frequency (v) and energy. Light of a particular wavelength (λ) has a particular frequency (v) and energy. E = h∙v and c = λ∙v E = h∙v and c = λ∙v c=3.0 x 10 8 m/s speed of light h=6.63 x joule-sec Plank’s constant

Why each element produces a unique line spectra?

Newtonian mechanics-describes objects at ordinary velocities (classical mechanics) Newtonian mechanics-describes objects at ordinary velocities (classical mechanics) Quantum mechanics- describes particles at velocities near that of light (subatomic particles). Quantum mechanics- describes particles at velocities near that of light (subatomic particles). Quantum- a packet of energy Quantum- a packet of energy

Heisenberg’s Uncertainty Principle It is impossible to know both the location and the velocity of an electron at the same time. It is impossible to know both the location and the velocity of an electron at the same time. - to “see” an electron we would have to bounce light off of it which would change its velocity.

Why did Werner Heisenberg hate driving cars? Because, every time he looked at the speedometer he got lost! Because, every time he looked at the speedometer he got lost!

Schrödinger Treated electrons as a wave Treated electrons as a wave Radial Probability for an electron The area of highest probability forms the electron cloud

Locating Electrons Principle quantum number (n) Sublevel (l) Orbital (m) Spin (s)

Principle quantum number (n) Energy levels are a particular distance from the nucleus electrons electrons n = n =

Principal Quantum Number (n) The maximum number of electrons at each energy level is 2n 2. The maximum number of electrons at each energy level is 2n 2. at n = 1, there can be 2(1) 2 =2 electrons at n = 2, there can be 2(2) 2 =8 electrons at n = 3, there can be 2(3) 2 =18 electrons

Sublevel (l) Tells the shape Tells the shape Each energy level has a number of sublevels equal to n. Each energy level has a number of sublevels equal to n. Energy level (n) sublevels 11s 22s,2p 3 3s,3p,3d 3s,3p,3d 44s,4p,4d,4f

Orbital Orientation (m) Each orbital can hold up to two electrons. Each orbital can hold up to two electrons. sublevel# orbitals# electrons s12 p36 d510 f714

“d” orbitals

Spin (s) indicates the direction of spin on the electron.  Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers. The two electrons in an orbital must have opposite spins. The two electrons in an orbital must have opposite spins.

Electron configuration notation He has 2 electrons, so its electron configuration would be 1s 2 1s 2 2s 1 1s 2 2s 2 2p 3 1s 2 2s 2 2p 6 1s 2 2s 2 2p 6 3s 1 or [Ne]3s 1 Principle quantum number sublevel No. of electrons Li N Ne Na

Degenerate orbitals have the same energy

1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f Sublevels fill in order of increasing energy. 1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f6d7p

Predicting electron configurations from the periodic table.

Aufbau Principle- electrons first occupy the lowest energy level available. Electron Dot Notation- show only the valence electrons, those in the outermost energy level. H∙ He: Li∙ Be: Mg:

Orbital notation 1s 2s 2p 1s 2s 2p N (7)  F (9)  Hund’s rule- orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin.

Principal quantum number sublevel Orbitals per sublevel Orbitals per energy level Electrons per sublevel Electrons per energy level 1s1122 2sp spd spdf

Excited state- electrons in a higher than normal energy state Excited state- electrons in a higher than normal energy state N: 1s 2 2s 2 2p 3 in ground state N: 1s 2 2s 2 2p 3 in ground state 1s 2 2s 2 2p 2 3s 1 or 1s 2 2s 2 2p 2 3s 1 or 1s 2 2s 2 2p 2 3p 1 in excited state 1s 2 2s 2 2p 2 3p 1 in excited state Ions- lost or gained electrons Ions- lost or gained electrons Anions are negatively charged, having gained Anions are negatively charged, having gained Cations are positively charged, having lost Cations are positively charged, having lost Na + 1s 2 2s 2 2p 6 3s 1 Na + 1s 2 2s 2 2p 6 3s 1 Cl - 1s 2 2s 2 2p 6 3s 2 3p 5 6 Cl - 1s 2 2s 2 2p 6 3s 2 3p 5 6

Filled and half-filled sublevels are more stable than partially filled sublevels. Filled and half-filled sublevels are more stable than partially filled sublevels.     _ _ 1s 2s 2p 3s 3p 3d 4s Thus Cr takes an electron from 4s to put one electron in each of its 3d orbitals and Cu takes a 4s electron to fill each of its 3d orbitals. Thus Cr takes an electron from 4s to put one electron in each of its 3d orbitals and Cu takes a 4s electron to fill each of its 3d orbitals.